1 1 Square Roots of Perfect Squares Math

1. 1 Square Roots of Perfect Squares Math 90

• For each shaded square: – What is its area? – Write this area as a product. – How can you use a square root to relate the side length and area?

Calculate the Area:

Calculate the side length

For the area of each square in the table… • Write the area as a product. • Write the side length as a square root.

Squaring vs. Square Rooting • Squaring and square rooting are opposite, or inverse opera – Eg. • When you take the square root of some fractions you will get a terminating decimal. – Eg. • These are all called RATIONAL numbers.

• When you take the square root of other fractions you will get a repeating decimal. – Eg. • These are all called RATIONAL numbers

1. 2 Square Roots of Non-Perfect Squares d

Introduction. . . • Many fractions and decimals are not perfect squares. • A fraction or decimal that is not a perfect square is called a non-perfect square. – The square roots of these numbers do not work out evenly! • How can we estimate a square root of a decimal that is a non-perfect square?

Here are 2 strategies. . . Ask yourself: “Which 2 perfect squares are closest to 7. 5? ” 7. 5 2 2. 5 7. 5 is closer to 9 than to 4, so 3 is closer to 3 than to 2. What would be a good approximation?

Strategy #2. . . • Use a calculator! • But, of course, you must be able to do both!

Example #1 • Determine an approximate value of each square root. close to 9 close to 4 We call these 2 numbers ‘benchmarks’. What does this mean?

Example #2 • Determine an approximate value of each square root. Your benchmarks! 0. 20 0. 25 0. 30 0. 36 0. 40 Of course, you can always use a calculator to CHECK your answer!

What’s the number? • Identify a decimal that has a square root between 10 and 11. If these are the square roots, where do we start? 121 100 10 120 11

Mr. Pythagoras Recall: 2 a + • Junior High Math Applet Remember, we can only use Pythagorean Theorem on RIGHT angle triangles! 2 b = 2 c

Practicing the Pythagorean Theorem First, ESTIMATE each missing side and then CHECK using your calculator. 7 cm x 5 cm 8 cm 13 cm x

Applying the Pythagorean Theorem 1. 5 cm 2. 2 cm 6. 5 cm The sloping face of this ramp needs to be covered with Astroturf. a) Estimate the length of the ramp to the nearest 10 th of a metre b) Use a calculator to check your answer. c) Calculate the area of Astroturf needed.

Let’s quickly review what we’ve learned today. . . • Explain the term non-perfect square. • Name 3 perfect squares and 3 nonperfect squares between the numbers 0 and 10. • Why might the square root shown on a calculator be an approximation?

Assignment Time! • Complete the following questions in your notebook. • Be prepared to discuss your answers in class. • Show all of your work!